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SCORPION-xisa [38]
3 years ago
8

Hello I need help with this, Don Manuel has 600m of fence to build a rectangular-shaped corral. You will take advantage of a ver

y long wall as one of the sides of the pen, that is, on the side of the wall you will not use fence. What should be the dimensions of the pen with maximum area among all those that use 600m of fence?​
Mathematics
1 answer:
Anton [14]3 years ago
5 0

Answer:  If the wall is 300 meters long, the dimensions of the fence with the maximum area will be 300 × 150 = 45000 m²

Step-by-step explanation:

try combinations in a chart

190 × (600-190)/2 = 38950  = 190 × 205       increasing area

200 × (600-200)/2 = 40000   = 200 × 200

220 × (600-220)/2 = 41800   == 220 × 190

240 × (600-240)/2 = 43200   == 240 × 180

260 × (600-260)/2 = 44200  == 260 × 170

280 × (600-280)/2 = 44800 .  == 280 × 160

<u>300 × (600-300)/2 = 45000  == 300 × 150</u>  Maximum Area

310 × (600-310)/2 = 44950 . == 310 × 145    decreasing area

320 × (600-320)/2 = 44800 . == 320 × 140    

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The area of room is 812 square feet, cost of carpet to cover the room is $6739.6 and the remaining square feet of carpet are covered by furniture is 203 square feet.

<h3>What is the area of trapezoid?</h3>

The area of the trapezoid is the space occupied by it on the two dimensional plane. The area of this figure is half of the product of height and sum of sides.

A=\dfrac{(a+b)h}{2}

Here, (a and b) are the base sides of the trapezoid and (h) is the height.

A room is shaped like a trapezoid which has the height of 28 feet and the length of sides as 23 ft and 35 ft. Thus, the area of it is,

A=\dfrac{(a+b)h}{2}\\A=\dfrac{(23+35)28}{2}\\A=812\rm\; ft^2

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Furniture covers 25% of the floor. Thus, the remaining square feet of carpet are covered by furniture is,

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